计量经济论文.doc

数学与统计学院计量经济学课题学术论文姓 名：学 号：专 业：统 计 学年 级：09 级指导教师：日 期： 2012年1月 计量经济学课题研究 -关于以下两道题的分析 摘要：根据相关资料我们得到了1980-2007年全社会固定资产投资总额X与工业总产值Y的具体数值，本课题研究通过应用Eviews软件对这些数据进行计算和分析。分析时，19782007年中国货物进、出口额的自然对数序列分别为LM、LX，对LX与LM序列进行单位根检验，检验它们的平稳性，检验LX与LM的单整性和协整性。如果LX与LM协整的，再估计LX关于LM的误差修正模型。本论文是研究对于上述问题的一个简析过程，其要求是序列的检验过程，修正模型的建立、估计和分析过程。 关键词：协整、自然对数序列、修正模型、分析、建立一、估计的假设检验问题：1980-2007年全社会固定资产投资总额X与工业总产值Y的统计资料如下表所示：单位：亿元年份全社会固定资产投资（X）工业增加值（Y）年份全社会固定资产投资（X）工业增加值（Y）1980910.91996.5199417042.119480.719819612048.4199520019.324950.619821230.42162.3199622913.529447.619831430.12375.6199724941.132921.419841832.92789.0199828406.234018.419852543.23448.7199929854.735861.519863120.63967.0200032917.740033.619873791.74585.8200137213.543580.619884753.85777.2200243499.947431.319894410.46484.0200355566.654945.5199045176858.0200470477.465210.019915594.58087.1200588773.677230.819928080.110284.52006109998.291310.9199313072.314188.02007137323.9107367.2试问：（1） 当设定模型为时，是否存在序列相关性？是否存在异方差性？（2） 若按一阶自相关假设，试用广义最小二乘法估计原模型；（3） 采用差分形式与作为新数据，估计模型，该模型是否存在序列相关？解析如下：（1）当设定模型为时，是否存在序列相关性？是否存在异方差性？序列相关性检验：用EVIEWS得到方程ln(y)=1.588+0.854*ln(x)R2=0.9932=0.992、 F=3610.878 、DW=0.379VariableCoefficientStd. Errort-StatisticProb.C1.588478116153860.13421958119077811.83492082199265.69432643209025e-12LOG(X)0.8544154372981840.014218790963478860.09058291192021.9810918249638e-29R-squared0.992851011528544Mean dependent var9.55225614467196Adjusted R-squared0.992576050433488S.D. dependent var1.30394757072632S.E. of regression0.112351179471786Akaike info criterion-1.46562532731656Sum squared resid0.328192475746238Schwarz criterion-1.37046786230405Log likelihood22.5187545824319F-statistic3610.8781546944Durbin-Watson stat0.379323139600627Prob(F-statistic)1.98109182496354e-291、序列相关性检验在显著性水平为5%的情况下，dl=1.33 du=1.48.DW=0.379dl.所以存在正自相关。从残差和时间的相关图（如下）也可以看出存在着序列相关。异方差检验：采用G-Q检验。将原始数据按x2排成升序，去掉中间的7个数据，得到两个容量为10的子样本，对两个子样本分别做最小二乘法回归，求各自的残差平方和。子样本一： 0.6907200011*LOG(X) + 2.806231214R2=0,962. RSS1=0.066267：VariableCoefficientStd. Errort-StatisticProb.C2.8062310.3765227.4530380.0001LOG(X)0.6907200.04906714.077030.0000R-squared0.961196Mean dependent var8.091034Adjusted R-squared0.956345S.D. dependent var0.435600S.E. of regressionR2Akaike info criterion-1.778769Sum squared resid0.066267Schwarz criterion-1.718252Log likelihood10.89385F-statistic198.1629Durbin-Watson stat0.604215Prob(F-statistic)0.000001VariableCoefficientStd. Errort-StatisticProb.C3.2349240.13933523.216930.0000LOG(X)0.7047650.01275755.243270.0000R-squared0.997385Mean dependent var10.92290Adjusted R-squared0.997059S.D. dependent var0.399824S.E. of regression0.021684Akaike info criterion-4.647613Sum squared resid0.003762Schwarz criterion-4.587096Log likelihood25.23806F-statistic3051.819Durbin-Watson stat0.973852Prob(F-statistic)0.000000子样本二由上表二得：LOG(Y) = 3.23492396 + 0.7047647956*LOG(X)R2=0.997.RSS2=.004计算F统计量：F=RSS2/SS1=0.06.在5%的水平下，自由度为（8、8）的F分布临界值为3.58.即接受原假设，两样本方差相同。G-Q检验以F检验为基础，适用于样本容量较大、异方差递增或递减的情况。还特检验则不需要排序，且对任何形式的异方差都可以检验。进行相应的怀特检验。如下可知在5%的原假设下我们接受原假设，及方差相同。VariableCoefficientStd. Errort-StatisticProb.C0.0696200.0927800.7503760.4600LOG(X)-0.0100960.020430-0.4941900.6255(LOG(X)20.0004060.0011020.3687260.7154R-squared0.114077Mean dependent var0.011721Adjusted R-squared0.043204S.D. dependent var0.011882X0.011623Akaike info criterion-5.970777Sum squared resid0.003377Schwarz criterion-5.828041Log likelihood86.59088F-statistic1.609586Durbin-Watson stat0.998111Prob(F-statistic)0.220012（4） 若按一阶自相关假设，试用广义最小二乘法估计原模型；VariableCoefficientStd. Errort-StatisticProb.E(-1)0.7665510.1143516.7034970.0000R-squared0.631825Mean dependent var-0.006975Adjusted R-squared0.631825S.D. dependent var0.105869S.E. of regression0.064239Akaike info criterion-2.616086Sum squared resid0.107292Schwarz criterion-2.568092Log likelihood36.31716Durbin-Watson stat1.126451E = 0.7665509335*E(-1)对原模型进行广义差分，可得Yt-0.7666Yt-1=（1-0.76655）+（Xt-Xt-1）+Ut上式进行广义回归，得到下表： VariableCoefficientStd. Errort-StatisticProb.C2056.499438.79434.6867040.0001X-0.7666*X(-1)0.7240550.02556728.319780.0000R-squared0.969771Mean dependent var9707.147Adjusted R-squared0.968561S.D. dependent var10133.06S.E. of regression1796.685Akaike info criterion17.89646Sum squared resid80701881Schwarz criterion17.99245Log likelihood-239.6022F-statistic802.0101Durbin-Watson stat0.408232Prob(F-statistic)0.000000方程为0.7666*Y(-1) = 2056.499094 + 0.7240551294*(X-0.7666*X(-1)在5%的情况下，DW检验拒绝原假设Dl=1.33.Du=.1.48.可知存在序列相关性。VariableCoefficientStd. Errort-StatisticProb.C889.3388260.88363.4089490.0022X10.5964130.02991619.936410.0000R-squared0.940823Mean dependent var3902.619Adjusted R-squared0.938456S.D. dependent var4453.815S.E. of regression1104.907Akaike info criterion16.92410Sum squared resid30520498Schwarz criterion17.02009Log likelihood-226.4753F-statistic397.4604Durbin-Watson stat0.960842Prob(F-statistic)0.000000二、时间序列的平稳性和协整检验问题观察中国货物进出口数据发现两者间有很强的同步性，由于中国的加工贸易占总贸易量的一半左右，一种观点认为中国的货物进口很大程度上受货物出口波动的影响。下表给出了19782007年中国货物进、出口额的自然对数序列LM，LX下表给出了19782007年中国货物进出口额的自然对数序列。年份LXLM年份LXLM19784.57994.690419936.82156.946619794.91715.054319947.09857.052819805.19965.299319957.30517.186019815.39415.394519967.32027.235819825.40815.262219977.51097.261019835.40405.365519987.51597.245919845.56615.613519997.57527.412819855.61136.046220007.82087.719119865.73466.061720017.88657.797919875.97746.068720028.08837.990119886.16376.314820038.38538.325519896.26426.382520048.68838.632719906.43126.279520058.93858.794719916.57806.458220069.17888.976519926.74456.692020079.40749.1653试问：（1） 对LX与LM序列进行单位根检验，检验它们的平稳性；（2） 检验LX与LM的单整性；（3） 检验LX与LM的协整性；（4） 如果LX与LM协整的，请估计LX关于LM的误差修正模型。解析如下：模型三：D(LM) = C(1) + C(2)*T + C(3)*LM(-1) + C(4)*D(LM(-1)Dependent Variable: D(LM)Method: Least SquaresDate: 01/09/12 Time: 15:45Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C1.7679650.7124772.4814340.0205T0.0524950.0208532.5174240.0189LM(-1)-0.3664560.153238-2.3914200.0250D(LM(-1)0.4131680.1912162.1607460.0409R-squared0.261758Mean dependent var0.146821Adjusted R-squared0.169478S.D. dependent var0.131779S.E. of regression0.120094Akaike info criterion-1.269523Sum squared resid0.346141Schwarz criterion-1.079208Log likelihood21.77333F-statistic2.836560Durbin-Watson stat1.832088Prob(F-statistic)0.059412Breusch-Godfrey Serial Correlation LM Test:F-statistic0.324929Probability0.574187Obs*R-squared0.390055Probability0.532270LM(1)= 0.390055 Breusch-Godfrey Serial Correlation LM Test:F-statistic1.145102Probability0.336439Obs*R-squared2.639983Probability0.267138LM(2)= 2.639983D(LM) = 1.767965206 + 0.05249476735*T - 0.3664563592*LM(-1) + 0.413168249*D(LM(-1)由于LM(1)= 0.390055 ，LM(2)= 2.639983，不存在自相关。模型二： D(LM) = C(1) + C(2)*LM(-1) + C(3)*D(LM(-1)Dependent Variable: D(LM)Method: Least SquaresDate: 01/09/12 Time: 15:57Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.0100450.1557840.0644800.9491LM(-1)0.0157650.0228280.6906070.4962D(LM(-1)0.1914770.1869731.0240910.3156R-squared0.066819Mean dependent var0.146821Adjusted R-squared-0.007836S.D. dependent var0.131779S.E. of regression0.132294Akaike info criterion-1.106624Sum squared resid0.437542Schwarz criterion-0.963888Log likelihood18.49273F-statistic0.895041Durbin-Watson stat1.896267Prob(F-statistic)0.421284D(LM) = 0.01004498345 + 0.0157648947*LM(-1) + 0.1914771663*D(LM(-1)LM(1)= 0.361347 LM(2)= 6.150377Breusch-Godfrey Serial Correlation LM Test:F-statistic0.313775Probability0.580565Obs*R-squared0.361347Probability0.547759Breusch-Godfrey Serial Correlation LM Test:F-statistic3.237096Probability0.057715Obs*R-squared6.150377Probability0.046181由于LM(1)= 0.390055 ，LM(2)= 2.639983，不存在自相关。由于模型残差项不存在自相关，因此模型是正确的。常数项的t统计量小于分布表的临界值，因此不能拒绝不存在常数项的零假设。模型一：D(LM) = C(1)*LM(-1) + C(2)*D(LM(-1)Dependent Variable: D(LM)Method: Least SquaresDate: 01/09/12 Time: 16:12Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LM(-1)0.0171930.0054233.1703020.0039D(LM(-1)0.1918120.1832861.0465190.3050R-squared0.066664Mean dependent var0.146821Adjusted R-squared0.030766S.D. dependent var0.131779S.E. of regression0.129736Akaike info criterion-1.177886Sum squared resid0.437615Schwarz criterion-1.082729Log likelihood18.49041Durbin-Watson stat1.899388D(LM) = 0.01719297554*LM(-1) + 0.1918124964*D(LM(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic0.262561Probability0.612864Obs*R-squared0.290893Probability0.589649Breusch-Godfrey Serial Correlation LM Test:F-statistic3.238267Probability0.056878Obs*R-squared5.950154Probability0.051043LM(1)= 0.290893，LM(2)= 5.950154，t统计量大于临界值，不能拒绝存在单位根的零假设。 所以LM序列是非平稳的。Lx单位根检验：模型三：D(LX) = C(1) + C(2)*T + C(3)*LX(-1) + C(4)*D(LX(-1)Dependent Variable: D(LX)Method: Least SquaresDate: 01/09/12 Time: 16:18Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.8881100.6313191.4067540.1723T0.0298650.0206451.4466390.1609LX(-1)-0.1825270.141088-1.2937100.2081D(LX(-1)0.3524080.2029831.7361450.0954R-squared0.208916Mean dependent var0.160368Adjusted R-squared0.110030S.D. dependent var0.095384S.E. of regression0.089984Akaike info criterion-1.846812Sum squared resid0.194330Schwarz criterion-1.656497Log likelihood29.85537F-statistic2.112706Durbin-Watson stat2.229623Prob(F-statistic)0.125113D(LX) = 0.888110451 + 0.02986532688*T - 0.182527306*LX(-1) +0.3524083158*D(LX(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic2.541338Probability0.124552Obs*R-squared2.785973Probability0.095093Breusch-Godfrey Serial Correlation LM Test:F-statistic3.332472Probability0.054424Obs*R-squared6.510336Probability0.038574LM(1)= 2.785973，LM(2)= 6.510336不存在自相关。模型二：D(LX) = C(1) + C(2)*LX(-1) + C(3)*D(LX(-1)Dependent Variable: D(LX)Method: Least SquaresDate: 01/09/12 Time: 16:25Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C-0.0138470.101293-0.1366980.8924LX(-1)0.0204870.0148721.3775900.1805D(LX(-1)0.2074700.1803511.1503690.2609R-squared0.139935Mean dependent var0.160368Adjusted R-squared0.071129S.D. dependent var0.095384S.E. of regression0.091929Akaike info criterion-1.834637Sum squared resid0.211275Schwarz criterion-1.691900Log likelihood28.68491F-statistic2.033778Durbin-Watson stat2.164247Prob(F-statistic)0.151930D(LX) = -0.01384655279 + 0.02048722078*LX(-1) + 0.2074698738*D(LX(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic1.746329Probability0.198799Obs*R-squared1.899192Probability0.168169Breusch-Godfrey Serial Correlation LM Test:F-statistic2.230898Probability0.130163Obs*R-squared4.549240Probability0.102836LM(1)= 1.899192，LM(2)= 4.549240不存在自相关。由于模型残差项不存在自相关，因此模型是正确的。常数项的t统计量小于分布表的临界值，因此不能拒绝不存在常数项的零假设。模型一：D(LX) = C(1)*LX(-1) + C(2)*D(LX(-1)Dependent Variable: D(LX)Method: Least SquaresDate: 01/09/12 Time: 16:32Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LX(-1)0.0185710.0048643.8181500.0007D(LX(-1)0.2054670.1763301.1652430.2545R-squared0.139292Mean dependent var0.160368Adjusted R-squared0.106188S.D. dependent var0.095384S.E. of regression0.090178Akaike info criterion-1.905318Sum squared resid0.211433Schwarz criterion-1.810161Log likelihood28.67445Durbin-Watson stat2.153919D(LX) = 0.01857058739*LX(-1) + 0.2054671843*D(LX(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic1.453044Probability0.239326Obs*R-squared1.537436Probability0.215000Breusch-Godfrey Serial Correlation LM Test:F-statistic1.755104Probability0.194361Obs*R-squared3.572168Probability0.167615LM(1)= 1.537436，LM(2)= 3.572168，t统计量大于临界值，不能拒绝存在单位根的零假设。 所以LX序列是非平稳的。（1） 检验LX与LM的单整性；LM的单整性检验：一阶单整性检验：D(D(LM) = C(1)*D(LM(-1)Dependent Variable: D(D(LM)Method: Least SquaresDate: 01/09/12 Time: 16:37Sample (adjusted): 3 30Included observations: 28 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(LM(-1)-0.3689130.138639-2.6609670.0130R-squared0.206630Mean dependent var-0.006254Adjusted R-squared0.206630S.D. dependent var0.168305S.E. of regression0.149912Akaike info criterion-0.922482Sum squared resid0.606784Schwarz criterion-0.874903Log likelihood13.91474Durbin-Watson stat1.933576D(D(LM) = -0.3689131591*D(LM(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic0.042670Probability0.837957Obs*R-squared0.000000Probability1.000000Breusch-Godfrey Serial Correlation LM Test:F-statistic1.509500Probability0.240487Obs*R-squared0.000000Probability1.000000LM(1)= 0.000000，LM(2)= 0.000000，不存在自相关，是1阶单整的。2阶单整性检验：D(D(D(LM) = C(1)*D(D(LM(-1)Dependent Variable: D(D(D(LM)Method: Least SquaresDate: 01/09/12 Time: 16:45Sample (adjusted): 4 30Included observations: 27 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D(D(LM(-1)-1.1204840.192862-5.8097720.0000R-squared0.564729Mean dependent var0.004663Adjusted R-squared0.564729S.D. dependent var0.255824S.E. of regression0.168780Akaike info criterion-0.684102Sum squared resid0.740658Schwarz criterion-0.636108Log likelihood10.23538Durbin-Watson stat2.130060D(D(D(LM) = -1.120483643*D(D(LM(-1)Breusch-Godfrey Serial Correlation LM Test:F-statistic6.660307Probability0.016116Obs*R-squared5.673417Probability0.017224Breusch-Godfrey Serial Correlation LM Test:F-statistic5.366394Probability0.011848Obs*R-squared8.337579Probability0.015471LM(1)= 5.673